Coordinate conversion calculator

ABSTRACT

A calculator for converting between sets of azimuth and elevation angular coordinates which define the same direction but which are with respect to different planes, the planes being related to each other by pitch and roll angles therebetween. The calculator includes a gimbal assembly, angular scales and cooperating pointers which form a mechanical analog of the direction, the planes, and the angles therebetween. When one set of angular coordinates and the pitch and roll angles between the planes are set into the calculator, the other set of angular coordinates is indicated thereby.

United States Patent Rapsilber et al.

[ 1 Feb. 8, 1972 [54] COORDINATE CONVERSION CALCULATOR [72] Inventors:William E. Rapsilber, 3621 McKibbon Road, St. John, Mo 63114; Richard G.

Koenig, 5114 l-lombert Road, Alton, 111. 62002 22 Filed: Dec. 8, 1969211 Appl.No.: 883,186

[52] US. Cl. 33/1 SA, 235/61 GM [51] Int. Cl. ..-.G01b 5/24 [58] FieldolSearch ..33/l R, 1 SA; 235/61 GM,61 NV [56] References Cited UNITEDSTATES PATENTS Webb ..33/ 1 SA 3,456,350 7/1969 Riblet et al ..33/l SA2,694,859 11/1954 Gwillam ..33/1 SA Primary Examiner-*William D. Martin,Jr. Attorney-Charles B. Haverstock [5 7] ABSTRACT A calculator forconverting between sets of azimuth and elevation angular coordinateswhich define the same direction but which are with respect to differentplanes, the planes being related to each other by pitch and roll anglestherebetween. The calculator includes a gimbal assembly, angular scalesand cooperating pointers which form a mechanical analog of thedirection, the planes, and the angles therebetween. When one set ofangular coordinates and the pitch and roll angles between the planes areset into the calculator, the other set of angular coordinates isindicated thereby.

15 Claims, 10 Drawing Figures PATENTED FEB 8 i972 SHEEI 1 OF 5PATENYEDFEB w: 3.639.989

SHEET 3 BF 5 J0 (9g 98 Ill.

COORDINATE CONVERSION CALCULATOR In certain geometrical problems it isdesirable to provide directional information in the form of azimuth andelevation angles to computer means so they can perform certainpredetermined operations thereon and arrive at solutions. In suchinstances, it is common to establish means which measure the elevationangle with respect to a nonstabilized platform and the azimuth anglewith respect to a predetermined line on the nonstabilized platform whichis taken as the azimuth line, and feed such information to the computermeans. To check the operation of the computer means with regards to acertain particular solution, it is sometimes desirable to refeed thesame directional information into the computer means at a later time andcompare the resultant solution with the original solution to see if avariance exists therebetween, which variance indicates that the computermeans are operating improperly. Unfortunately the set of azimuth andelevation angles with respect to the nonstabilized platform which wasfed to the computer means at a given instant is sometimes difficult orimpossible to obtain directly, while a set of azimuth and elevationangles of the same direction with respect to a stabilized platform andthe pitch and roll angles between the stabilized and nonstabilizedplatforms are relatively easy to obtain. When the two platforms have 0azimuth lines thereon which always lie on a plane that is projectedperpendicularly from the stabilized platform, the two sets of azimuthand elevation angles mentioned above with respect to the stabilized andnonstabilized platforms are related by the equations:

A tancos E sin A cos cos E, cos A, sin 6 sin sin E, cos 6 sin cos E, cosA, cos 6+ sin E, sin 6 coordinates with respect to the other platformare then indicated by other scales and pointers also associated with thedirection simulating means and hence the desired angular coordinateconversion is accomplished. This can be done simply and mechanicallyusing the subject device. Even though the primary purpose of the subjectcalculator is to solve the above stated equations for k, and A thecalculator can also be used to find any two of the six variables (1\,,,A E,, A,, 6, (1:) which appear in the equations once the other four areknown and set therein or it can be used as a visual teaching aid todemonstrate the angular relationships between various planes and vectorstherefrom.

It is therefore a principal object of the present invention to providemeans for converting between different sets of angular coordinates.

Another object of the present invention is to provide angular coordinateconversion means which are accurate and relatively inexpensive.

It is another object of the present invention to provide coordinateconversion means which are easy to operate and which require relativelylittle skill and training to operate.

Another object of the present invention is to provide an angularcoordinate calculator which is mechanical in nature and which requiresno outside power source.

Another object of the present invention is to provide means forreconstructing input information fed to computer means for use inchecking the outputs and hence the operation and accuracy of thecomputer means.

Another object of the present invention is to provide means where:

A is the azimuth angle of the direction relative to the 0 azimuth lineon the nonstabilized platform,

A, is the elevation angle relative to the nonstabilized platform,

A. is the azimuth angle relative to the 0 azimuth line on the stabilizedplatform,

E, is the elevation angle relative to the stabilized platform 6 is thepitch angle of the 0 azimuth line on the nonstabilized platform relativeto the 0 azimuth line on the stabilized platform, and

42 is the roll angle of the nonstabilized platform relative to thestabilized platform,

and therefore it is possible to convert from one set of angularcoordinates to the other. To do so by hand, however, as can be surmisedfrom the equations is time consuming and tedious, and the chance forhuman error is large. The coordinate conversion can also be accomplishedthrough the use of elec tronic computers but computers sophisticatedenough to handle the above equations are relatively expensive and alsorequire power sources and therefore are not suitable for certainapplications including those in remote locations.

The disadvantages and shortcomings of the methods and means heretoforeemployed to convert between sets of angular coordinates such as thoserelated by the above equations are solved by the present device which isa relatively inexpensive device, requiring no power source, and whichproduces acceptably accurate results.

The subject calculator includes a mechanical gimbal as sembly and asystem of scales and pointers which allow a mechanical analog of thedesired geometrical problem to be set up. The gimbal assembly ismanipulated by adjustment means associated therewith until it simulatesthe known pitchand-roll relationships that existed between the twoplatforms at the given instant for which the set of coordinates withrespect to one of the platforms is known. Portions of the gimhalassembly are then adjusted until certain scales and pointers associatedtherewith indicate that the desired physicalrelationship exists betweendirection simulating means included with the gimbal assembly and theplatform from which the known angular coordinates were measured. Theangular for converting easily observable angular coordinates of adirection into angular coordinates of a different angular coordinatesystem which are relatively more difficult to observe or discover.

Another object of the present invention is to provide means for visuallydisplaying the difi'erences between selected sets of coordinates ofdifferent coordinate systems so that the differences and interactionstherebetween can be easily visualized.

These and other objects and advantages of the present invention willbecome apparent after considering the following detailed specificationswhich covers a preferred embodiment thereof in conjunction with theaccompanying drawings wherein:

FIG. I is a side elevational view of the subject calculator showing theoperative portions thereof in their centered positions;

FIG. 2 is a cross-sectional view of the subject calculator taken at line2-2 of FIG. 1;

FIG. 3 is an enlarged fragmentary cross-sectional view taken at line 33of FIG. 2;

FIG. 4 is an enlarged fragmentary cross-sectional view taken at line 4-4of FIG. 2;

FIG. 5 is an enlarged fragmentary cross-sectional view taken at line 55of FIG. 2;

FIG. 6 is a cross-sectional view of the subject calculator taken at line66 of FIG. 1;

FIG. 7 is an exploded view of the gimbal assembly of the subjectcalculator showing the scales, indicators, pointers and pivotsassociated therewith;

FIG. 8 is a cross-sectional view taken at line 8-8 of FIG. 6;

FIG. 9 is an enlarged fragmentary view of a portion of FIG. 8; and,

FIG. I0 is a perspective view of the subject calculator showing themovable parts thereof in different positions for solving coordinateconversion problems.

Referring to the drawings more particularly by reference numbers, thenumber 10 in FIG. 1 refers to an angular coordinate conversioncalculator constructed according to the present invention. Thecalculator 10 includes a fixed and scaled transparent coordinate member12, a gimbal assembly 14 and supporting structure 16 for the variouscomponents of the calculator. The supporting structure I6 includes abase 18, a lower coordinate member support block 20 connected thereto,and an upper support member 22 which is supported above and at an angleto the base 18 by upstanding members '24 and 26. The supportingstructure 16 also includes a pitch indicator pointer 28 and a support 30therefor which pointer 28 will be discussed more in detail later.

The coordinate member 12 is fixed in a predetermined positionwithrespect to the gimbal assembly 14 and the pitch indicator pointer 28 bythe lower coordinate member support block 20 and the upper supportmember 22 to which it is attached. Lines 32 and 34 are inscribed on theinner or outer surface of the coordinate member 12 to form elevation andazimuth scales thereon. The lines 32 and 34 represent elevation andazimuth angles which correspond to the angular coordinates E, and A, inthe above stated equations which are of course the angular coordinateswith respect to the stabilized platform which will be described more indetail hereinafter. The coordinate member 12 is preferably constructedto be a segment of a sphere and when so constructed the elevation lines32 and the azimuth lines 34 inscribed thereon correspond to or aresimilar to latitude and longitude lines on a globe. The lines 32 and 34are shown calibrated in degrees although radians or any other suitableangular measure could be used as is also true with all of the scalesassociated with the subject calculator 10.

The center 36 of the coordinate member 12 is the point for both theelevation and azimuth scales, and for convenience the elevation andazimuth scales extend 60 in all directions from the 0 point as shown.The 120 range of angles defined by the scale lines 32 and 34 can beincreased or decreased without substantial modification to thecalculator If) as desired. The elevation lines 32 above the 0 elevationline are indicated as being positive while the elevation lines 32 belowthe 0 elevation line are negative elevation lines The azimuth lines 34shown in FIG. 1 which are to the left of the 0 azimuth or heading linewhen looking at the coordinate member 12 from the convex or front sidethereof represent positive azimuth angles from the aforementioned 0azimuth line on the stabilized platform while the lines 34 on the rightside of the 0 azimuth line indicate negative azimuth angles therefrom.The portions of the scales on the coordinate member 12 which arepositive or negative can be arbitrarily chosen initially as long as theother scales of the calculator to be described are assigned positive andnegative signs which are consistent therewith, and it should beremembered that this specification describes only only one of manypossible consistent arrangements for the polarities of the scales. Thecoordinate member 12 and the selected portions of the supportingstructure 16 are preferably constructed from a transparent material suchas Plexiglas so that the gimbal assembly I4 and the scales on thecoordinate member 12 are visible in all positions of the members.

The upper support member 22 which supports the upper portion of thecoordinate member 12 includes an opening 38 through the center portionthereof. The gimbal assembly 14 is spaced from and is pivotallysupported in the opening 38 by spacers 39 (FIG. 8) and by a pair ofaxially aligned journals 40 and 42 whose axes are horizontal to the base18 and which pass through the center of motion 43 of the gimbal assemblyI4. The stabilizer platform is not present physically in the subjectdevice but it can be visualized by imagining a plane 44, which is shownin FIG. 10, extending from the pitch indicator pointer 28 to the 0elevation line on the coordinate member 12. The axes of the journals 40and 42 and the center of motion 43 all lay on this imaginary, stabilizedplatform simulating plane 44. The entire gimbal assembly 14 is rotatableabout the journals 40 and 42 and hence with respect to the imaginaryplane 44 to thereby enter the pitch angle infonnation 6 into thecalculator 10. The assembly 14 can be manually rotated or it can berotated by means of optional pitch angle adjustment means 45 which areshown as a gear assembly associated with the journal 42 (FIG. 8) andwhich will be described more in detail hereinafter.

Referring to FIG. 7 which is an exploded view of the gimbal assembly 14,the gimbal assembly 14 includes outer, middle and inner gimbal members46, 48 and 50 respectively, and a coordinate pointer 52 which make upthe operative portions thereof. The outer gimbal member 46 includes aflat annular ring portion 54 which is pivotally mounted to the uppersupport member 22 by the aforesaid aligned journals 40 and 42 so thatthe axes thereof are coexistent with a diameter of the ring portion 54.An annular roll scale 56 calibrated in degrees is positioned on one orboth flat surfaces of the ring portion 54. As shown, the roll scale 56is oriented so the and the -90 indications thereof are located adjacentto the journals 40 and 42 respectively, and the 0 indications thereofare located on a diameter of the ring portion 54 which is at rightangles'to the diameter on which the +90 and 90 indications are located.The roll scale 56, although shown in FIG. 6 as being calibrated from 0at the top thereof through i90 and back to 0 at the bottom thereof, canalso be calibrated from 0 at the top to i at the bottom for conveniencein solving problems where the stabilized and nonstabilized platforms areoriented with a roll angle of more than 90 therebetween. These lastmentioned problems can of course be solved with the calculator 10 asshown by mental conversions of the roll angles as required. Extendingoutwardly from the 0 indications of the roll scale 56 and at rightangles to the ring portion 54 is a flat semicircular ring portion 62which includes a pitch scale 64 on one or both sides thereof. The pitchscale 64 is calibrated in degrees from -i90 to 90 with the 0 indicationthereof on a radius which bisects the semicircular ring portion 62. Asshown in FIG. 1, positive pitch angles are indicated on the uppersegment or half of the portion 62 while negative pitch angles areindicated on the lower segment thereof. The pitch scale 64 cooperateswith the aforementioned pitch indicator pointer 28 to indicate the pitchangle 6 at which the nonstabilized platform simulating portion of thegimbal assembly 14 is pivoted with respect to the aforesaid stabilizedplatform simulated by the imaginary plane 44. The pitch indicatorpointer 28 is fixed by the supporting structure 16 and is alwaysadjacent to the semicircular ring portion 62 because the longitudinalaxis of the pointer 28 extends through the center of motion 43 of theassembly 14 and is at a right angle to the axes of the journals 40 and42 on which the gimbal assembly 14, of which the semicircular ringportion 62 is a part, pivots. The pointer support 30 may include meanssuch as a set screw S which allows longitudinal adjustment of thepointer 28 so that the end 65 thereof can be adjusted into as close aproximity to the semicircular ring portion 62 as desired.

The optional pitch adjustment means 45 as aforesaid enable preciseadjustment of the pitch angle 0 between the stabilized and nonstabilizedplatform simulating means employed in the subject calculator 10. Thepitch adjustment means 45 which are shown in detail in FIGS. 2 and 3include a knob 66 journaled for rotation in a portion of the upstandingmember 26 and in a portion of the upper support member 22. Turning theknob 66 rotates the gimbal assembly members 46, 48 and 50 as a unitthrough a shaft 67, which has a bevel gear 68 on the opposite endthereof from the knob 66. Another bevel gear 69 is mounted on the end ofanother shaft 70 and it meshes with gear 68. Mounted on the other end ofshaft 70 is a gear 71 which meshes with gear 72 which is secured to thering portion 54 of gimbal member 46.

As shown in detail in FIGS. 8 and 9 the inner edge of the annular ringportion 54 includes an annular V-shaped groove 74 which is positioned inopposition to a similar annular V- shaped groove 76 formed in the outeredge of another flat annular ring portion 78 which is part of the middlegimbal member 48. The grooves 74 and 76 are held in alignment by bearingmeans which can be a plurality of ball hearings or the long flexiblecylindrical member 80 as shown. The cylindrical member 80 may beconstructed from any suitable bearing material such as Nylon and it isplaced between the grooves 74 and 76 through a bore 81 (FIG. 6) whichextends through the annular ring portion 54 to the groove 74. Thegrooves 74 and 76 and the member 80 therebetween enable coplanarconcentric rotation between the outer and middle gimbal members 46 and48 so that a roll angle d: can be established therebetween.

The ring portion 78 of the gimbal member 48 includes two roll indicatorpointers 82 located on a diameter thereof and on one or both oppositesides thereof. The roll indicator pointers 82 cooperate with the rollscale or scales 56 on the outer gimbal member 46 to indicate the rollangle (ii of the nonstabilized platform with respect to the stabilizedplatform represented by the plane 44.

The middle and inner gimbal members 48 and 50 can be rotated as a unitto establish a roll relationship between the two platforms manually bymoving the members themselves or by means of optional roll adjustmentmeans 84 which are shown in FIGS. 2 and 5 connected between the outerand middle gimbal members 46 and 48. The roll adjustment means 84include a knob 86 rotatably mounted on the support members 22 and 24,which is connected by a flexible drive shaft 88 to a pinion gearassembly 90 mounted on the outer gimbal member 46. The pinion gearassembly 90 when rotated by the rotation of the knob 86 drives a rackgear 92 formed on the outer edge of the middle gimbal member 48 torotate it with respect to the outer gimbal member 46 to establish thedesired roll relationship therebetween. The rack gear 92 is shownextending through an arc of I80 which allows roll adjustment of 90 toeither side of the 0 roll position. If the roll scale 56 is calibratedto extend to plus and minus 180 rack gear 92 can be constructed toextend completely around the middle gimbal member 48 thus allowing 360of roll adjustment.

The middle gimbal member 48 also includes a semicircular ring portion 93which extends outwardly at a right angle to the ring portion 78 on adiameter thereof as shown in FIG. 7. The semicircular ring portion 93includes an azimuth (A indicator pointer 94 on its bisecting radiuswhich pointer cooperates with an azimuth (A scale 96 on a portion of theinner gimbal member 50 which will be described hereinafter. Thesemicircular ring portion 93 is the portion of the subject calculatorwhich physically simulates the nonstabilized platform. As can be seen inFIG. I the ring portion 93 is coexistent with the imaginary stabilizedplatform 44 when the pitch angle 9 and the roll angle 41 therebetweenare 0. By changing the pitch and roll angles, any desired relationshipcan be established between the two platforms.

The middle gimbal member 48 (FIGS. 4 and 7) also includes journals 97and 98 which are axially aligned on the same diameter thereof as thediameter on which the roll indicator pointers 82 are positioned. Thejournals 97 and 98 pivotally connect the inner gimbal member 50 to themiddle gimbal member 48. Spacer members 99 are provided with the 5direction of interest with respect to the nonstabilized platform whilethe elevation scale 106 cooperates with an elevation indicator pointer108 on the coordinate pointer 52 (FIGS. 1 and 7) to indicate theelevation angle h of the direction of interest with respect to the samenonstabilized platform.

The coordinate pointer 52 which is the direction simulating portion ofthe present invention is mounted in the center of the ring portion onjournals 110 and 111 (FIG. 7) which are axially aligned with thediameter of the ring portion 100 at the locations thereon from which thefirst semicircular ring portion 102 extends. The coordinate pointer 52is mounted for axial rotation about the journals I10 and 111 and spacedby spacers 112 in such a manner that the axis 113 of the coordinatepointer 52 (FIG. 8), which simulates the aforesaid direction, alwayspasses through the center of motion 43 of the gimbal assembly 14. Thecoordinate pointer 52 includes the aforementioned elevation indicator108 which is aligned with the axis 113 of the coordinate pointer 52 andwhich is formed in a cutout 114 in the coordinate pointer 52 adjacent toa transverse channel or groove 115 in which the second semicircular ringportion 104 of the inner gimbal member 50 and its associated elevationscale 106 slides. The outermost extremity of the coordinate pointer 52includes means aligned on the axis 113 including an outwardly biasedpointer member 116 which cooperates with the coordinate member 12 toindicate the azimuth and elevation angles A and E, of the direction ofinterest (which is the direction in which the pointer 52 is pointing)with respect to the stabilized platform. The biased pointer member 1 16preferably include an antifriction tip 118 constructed of a materialsuch as Nylon so it will not scratch the coordinate member 12 when it ismoved from one position thereon to another. The pointer member 116 alsoincludes a shaft portion 120 which extends into a bore 121 in the bodyportion 122 of the coordinate pointer 52. As shown in FIG. 8, a spring124 is located in the bore 121 between the bottom thereof and the shaftportion 120 to outwardly bias the pointer member 116 into engagementwith the member 12. Means such as slot and pin 125 can also be includedto retain the pointer 116 in the coordinate pointer 52. The coordinatepointer 52 may also include counter balance means 126 located on theopposite end thereof from the pointer 116 to minimize any tendency forthe coordinate pointer 52 to move once it has been set in a desiredposition. The counter balance means 126 are shown threadably attached tothe body 122 of the coordinate pointer 52 but they may be otherwiseattached thereto or even constructed integrally therewith, if desired.

Although as aforesaid the calculator 10 can be used to solve theequations:

cos E, sin A cos cos E cos A sin 0 sin sin E.- cos 0 sin d) journals tomaintain a proper operating clearance between the members 48 and 50.

The inner gimbal member 50 includes a flat annular ring portion 100 andtwo semicircular ring portions 102 and 104. The first semicircular ringportion 102 extends outwardly at right angles from the ring portion 100and at right angles from the diameter thereof which is aligned with theaxes of the journals 97 and 98 and it has the aforementioned azimuth(A,) scale 96 formed thereon. The second semicircular ring portion 104extends outwardly at right angles to the ring portion 100 but on theopposite side of the ring portion 100 from the first semicircularportion 102, and the portion 104 is aligned with the axes of thejournals 97 and 98. The second semicircular ring portion 104 has anelevation scale 106 formed thereon. Both scales 96 and 106 are showncalibrated in degrees and both have their 0 marks on radii thereof whichbisect the respective semicircular ring portions 102 and 104.

for any two of the six variables (A h A E,, 0, 4:), it is normallyexpected that the calculator will be used to solve for A and h when A,,E, 0 and (I) are known.

FIG. 10 shows an example of a coordinate conversion using the subjectcalculator when the known quantities are:

E,=38 To perform this conversion using the subject calculator 10, thegimbal assembly 14 is first pivoted manually, or by means of theoptional pitch adjustment means 45, until the known pitch angle 0 whichis 33 on the pitch scale 64 is aligned with the pitch indicator pointer28. This establishes a 33 pitch angle between the imaginary plane 44which simulates the stabilized platform and the semicircular ringportion 93 which simulates the nonstabilized platform.

The middle and inner gimbal members 48 and 50 are then rotated as a unitmanually, or by means of the optional roll adjustment means 84 until theroll indicator pointers 82 (more clearly seen in H6. 6) on the middlegimbal member 48 are aligned with the known roll angle d) of 31 on theroll scale 56 which is located on the ring portion 54 of the outergimbal member 46. This establishes a 3 1 roll angle between thestabilized and nonstabilized platform simulating means 44 and 93 whilemaintaining the same heading orientation for both.

The point on the coordinate member 12 which corresponds to the knownazimuth and elevation angles A,=33 an E,=38 of the desired directionwith respect to the simulated stabilized platform is then located on themember 12 by means of the elevation and azimuth lines 32 and 34 thereon.This point is marked in some convenient fashion such as with a markingpencil (not shown). The coordinate pointer 52 is then moved until thetip 118 of the pointer 116 abuts the coordinate member 12 at the markedpoint corresponding to the angles A,,=33 and E,=38. The coordinatepointer 52 is now at a point where it is simulating the desireddirection with respect to both the nonstabilized and the stabilizedplatforms. The azimuth angle A, of the desired direction with respect tothe nonstabilized platform is then indicated by the relative positioningof the azimuth indicator 94 on the middle gimbal member 48 and theazimuth scale 96 on the inner gimbal member 50 and is shown as beingapproximately 26. The elevation angle A, of the desired direction withrespect to the nonstabilized platform is indicated by the relativepositioning of the elevation indicator 108 which is part of thecoordinate pointer 52 and the elevation scale 106 on the inner gimbalmember 50 and is shown as being approximately Of course, by setting thepitch and roll angles 0 and d) and by moving the coordinate pointer 52until the indicator pointers 94 and 108 and the associated scales 96 and106 indicate known angles k and A, and thereafter by observing theresulting position of the coordinate pointer 52 with respect to thecoordinate member 12, the coordinate conversion can be accomplished inthe other direction to find the angles A, and E,. Although some trialand error manipulation and some practice may be required to obtain thedesired results, it is possible with the subject coordinate conversioncalculator means to find any two of the variables k k A E,,, 0 and 4) ifthe other four are known.

There are many possible uses and applications for which calculators suchas the present calculator could be used, and it is not intended torestrict or limit the subject device to any particular use orapplication. For example, it can be used to solve navigational andastronomical problems where information referenced to one set ofcoordinates needs to be quickly space with respect to a first plane inspace and with respect to a second plane in space where the second planecan be oriented in different known orientations relative to the firstplane about a common point fixed in said planes, said line extendingthrough said common point, comprising platform means establishing afirst coordinate system including the position and orientation of saidfirst plane, means movable relative to the platform means forestablishing any desired orientation of said second plane with respectto the first plane, said movable means including means for producingangular displacement of the second plane about two mutuallyperpendicular axes that pass through said common point, one of said axeslying in said first plane, cooperative means associated with saidplatform means and said movable means to indicate the angularorientation of the second plane relative to the first plane, other meansmovably associated with said platform for establishing and indicatingthe orientation of the line in said first coordinate system and withrespect to said first plane, and other means associated with the movablemeans for establishing the orientation of the second plane forindicating the angular coordinates of the line with respect to thesecond plane.

2. The means defined in claim 1 wherein said platform means forestablishing the position and orientation of the first plane include asupport structure and a scale member fixedly attached thereto, saidscale member having scales thereon calibrated to indicate the angularcoordinates of the said line with respect to said first plane.

3. The means defined in claim 2 wherein said scale member is constructedfrom a transparent material having a portion of a spherical surfacethereon on which the said scales are located.

4. The means defined in claim 2 wherein said means producing angulardisplacement of the second plane include a gimbal assembly having atleast two relatively movable gimbal members, the first of which isjournaled to said support structure for angular movement with respectthereto about one of said axes, said second gimbal member being joumaledto said first gimbal member for angular movement with respect thereofand about the other of said axes.

5. The means defined in claim 4 wherein said gimbal assembly includes apointer to indicate the direction of said line, and a third gimbalmember joumaled for angular movement relative to said second gimbalmember, said third gimbal member having scales thereon which cooperatewith said second gimbal member and with said pointer to indicate theangular coordinates of said line with respect to said second plane.

6. Mechanical calculator means for indicating any two of six variablesin the equations cos E, sinA, cos cos E, cosA, sin 6 sin 5 sin E, cos 0sin 5 k sin- (cos E, sinA, sin cos E cos A sin Q cos l sin E,co s 6 cosg and accurately converted to a different coordinate system, and to thisend it can be used to solve various sighting, guidance and related typesof problems. Also with minor changes the subject device including thevarious movable elements could be made to generate output signals torepresent their position for feeding to a computer which is programmedto solve for the desired unknowns depending on the type of solutiondesired. Also various changes could be made to the subject calculatorwhich will be apparent to those skilled in the art without departingfrom the spirit and scope of the invention including using other formsof pointers and indicator means, using a recalibrated flat coordinatemember instead of one that is spherical in form, and using other formsof positioning means between the various components thereof to name justa few. All such changes, including variations, modifications, andadaptations thereof which do not depart from the spirit and scope of theinvention are deemed to be covered by the invention which is limitedonly by the claims which follow.

What is claimed is:

1. Means for indicating the angular coordinates of a line in when theother four variables are set in said means, where the variables A, and Aare azimuth angles of a direction in space in first and secondcoordinate systems respectively, the variables E, and h are elevationangles of the same direction in space with respect to said first andsecond coordinate systems respectively, and the variables 6 and q' areperpendicular angular relationships defining the angular relationshipsbetween the two coordinate systems, including support structure meansestablishing the first coordinate system including establishing a firstrelatively fixed plane of reference for said first coordinate system,movable means associated with said support structure means forestablishing the second coordinate system including establishing asecond plane of reference that intersects the first plane of referenceat a common point in both said first and second planes of reference,adjustment means associated with said support structure means forestablishing the direction in space with respect to said first andsecond planes of reference, said direction in space passing through saidcommon point, first and second scale means including cooperatingrelatively movable members associated with the support structure meansand with the movable means associated therewith for indicatingrespectively the angles and d) between the first and second planes ofreference, third and fourth scale means including cooperating relativelymovable members associated with the support structure means and with theadjustment means for indicating respectively the azimuth angle A, andelevational angle E, of said direction in space with respect to saidfirst plane of reference, and fifth and sixth scale means includingcooperating relatively movable members associated with the movable meansand with the adjustment means for indicating respectively the azimuthangle A and the elevation angle A of said direction in space withrespect to said second plane of reference, any to unknown variables ofsaid six variables being indicated by their respective scale means whenthe other four scale means are indicating the other four variables.

7. The means defined in claim 6 wherein said means for establishing thefirst plane of reference include a transparent member on which saidthird and fourth scale means are located.

8. The means defined in claim 7 wherein said transparent member isshaped and positioned so that all points at which said third and fourthscale means are located thereon are equidistant from said common point.

9. The means defined in claim 6 wherein said means for establishing saidsecond plane of reference include a gimbal assembly on which said first,second, fifth and sixth scale means are located.

10. Means for converting between a set of known and a set of unknowncoordinates, one set being the azimuth and elevation angles of adirection with respect to a first plane and the other set being theazimuth and elevation angles of the same direction with respect to asecond plane whose orientation is related to the orientation of thefirst plane by known angles established therebetween about two mutuallyperpendicular axes, said coordinate converting means including a gimbalassembly defining a center point therein through which saidperpendicular axes pass, said gimbal assembly including means tosimulate the aforesaid direction which passes through said center point,said gimbal assembly also including other means to simulate said secondplane, said other means being supported for movement about said centerpoint, scale means positioned to be intersected by said simulateddirection including a first set of scales, a portion of said first setof scales establishing the position of said first plane, said first setof scales being calibrated to indicate the azimuth and elevation anglesof said direction from said center point and relative to said firstplane, means associated with said gimbal assembly to establishpredetermined orientations of said second plane with respect to saidfirst plane, a second set of scales located on said gimbal assembly forindicating the angular relationships in azimuth and elevation angles ofsaid direction with respect to said second plane, said converting meansindicating the unknown set of coordinates when the known set ofcoordinates and the orientation of the second plane with respect to thefirst plane are established.

ll. The means defined in claim 10 wherein said means to establishpredetermined orientations of said second plane with respect to saidfirst plane include first and second gear assemblies, said first gearassembly being movable to angularly rotate said means to simulate saidsecond plane about one of said mutually perpendicular axes and saidsecond gear assembly being movable to rotate said means to simulate saidsecond plane about the other of said mutually perpendicular axes.

12. The means defined in claim 10 wherein said first set of scalesincludes a scale for indicating the azimuth angle of said direction withrespect to said first plane which scale is formed by a family of lineswhich are the lines of intersection between said scale means and afamily of coaxial planes whose common axis passes through said centerpoint at right angles to said first plane.

13. The means defined in claim 10 wherein said first set ofscalesjncludes a scale for indicating the elevation angle of saiddirection with respect to said first plane which scale 15 formed by afamily of lines which are the lines of intersection between said scalemeans and a family of parallel planes including said first plane.

14. The means defined in claim 10 wherein said means for simulating thedirection include a pointer member pivotally connected to said gimbalassembly, said pointer member having means thereon engageable with saidscale means to indicate the set of coordinates of said direction inspace relative to said first plane, and wherein said gimbal assemblyincludes means thereon which cooperate with said pointer member toindicate the set of coordinates of said direction in space relative tosaid second plane.

15. The means defined in claim 14 wherein said pointer member iscounterbalanced.

Patent No. 316391989 Dated February 8, 1972 Inventor(s) William E.Rapsilber & Richard E. Koenig It is certified that error appears in theabove-identified patent and that said Letters Patent are herebycorrected as shown below:

On the Title Page, show the "Assignee McDonnell Douglas Corporation, St.Louis, Missouri".

Column 2, line 7 "l should be "l Column 5, line 31, after "180" insert"the"; line 68 5 (A1 should be (l Column 7 line 19, "33" should be "33".

Column 8, line 39 "thereof" should be "thereto".

Signed and sealed this 12th day of September 1972.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissionerof Patents FORM FO-105O (IO-6 USCOMM DC 60376-F69 =5 u MJVERNMENTPRINTING OFFICE (969 u-sssflsa UNITED STATES PATENT oTTTcE CERTIFICATEOF CQRECTEON Patent NO. 39,989 Dated February 8, 1972 Inventor(s)William E. Rapsilber & Richard E. Koenig It is certified that errorappears in the above-identified patent and that said Letters Patent arehereby corrected as shown below:

On the Title Page, show the "Assignee McDonnell Douglas Corporation, St.Louis, Missouri" Column 2, line 7, "A should be "l Column 5, line 31,after "180" insert "the"; line 68, (X1) should be (l Column 7, line 19,"33" should be "33".

Column 8, line 39, "thereof" should be "thereto".

Signed and sealed this 12th day of September 1972.

(SEAL) Attest';

EDWARD M .FLETCHER,JR. ROBERT GOTTSCHALK Attesting Officer Commissionerof Patents FORM l30-1050 USCOMM-DC 60376-F5 U S (-UVERNMEN] PRINHNGOFFICE 1959 0-355-334

1. Means for indicating the angular coordinates of a line in space withrespect to a first plane in space and with respect to a second plane inspace where the second plane can be oriented in different knownorientations relative to the first plane about a common point fixed insaid planes, said line extending through said common point, comprisingplatform means establishing a first coordinate system including theposition and orientation of said first plane, means movable relative tothe platform means for establishing any desired orientation of saidsecond plane with respect to the first plane, said movable meansincluding means for producing angular displacement of the second planeabout two mutually perpendicular axes that pass through said commonpoint, one of said axes lying in said first plane, cooperative meansassociated with said platform means and said movable means to indicatethe angular orientation of the second plane relative to the first plane,other means movably associated with said platform for establishing andindicating the orientation of the line in said first coordinate systemand with respect to said first plane, and other means associated withthe movable means for establishing the orientation of the second planefor indicating the angular coordinates of the line with respect to thesecond plane.
 2. The means defined in claim 1 wherein said platformmeans for establishing the position and orientation of the first planeinclude a support structure and a scale member fixedly attached thereto,saiD scale member having scales thereon calibrated to indicate theangular coordinates of the said line with respect to said first plane.3. The means defined in claim 2 wherein said scale member is constructedfrom a transparent material having a portion of a spherical surfacethereon on which the said scales are located.
 4. The means defined inclaim 2 wherein said means producing angular displacement of the secondplane include a gimbal assembly having at least two relatively movablegimbal members, the first of which is journaled to said supportstructure for angular movement with respect thereto about one of saidaxes, said second gimbal member being journaled to said first gimbalmember for angular movement with respect thereto and about the other ofsaid axes.
 5. The means defined in claim 4 wherein said gimbal assemblyincludes a pointer to indicate the direction of said line, and a thirdgimbal member journaled for angular movement relative to said secondgimbal member, said third gimbal member having scales thereon whichcooperate with said second gimbal member and with said pointer toindicate the angular coordinates of said line with respect to saidsecond plane.
 6. Mechanical calculator means for indicating any two ofsix variables in the equations when the other four variables are set insaid means, where the variables As and lambda a are azimuth angles of adirection in space in first and second coordinate systems respectively,the variables Es and lambda e are elevation angles of the same directionin space with respect to said first and second coordinate systemsrespectively, and the variables theta and phi are perpendicular angularrelationships defining the angular relationships between the twocoordinate systems, including support structure means establishing thefirst coordinate system including establishing a first relatively fixedplane of reference for said first coordinate system, movable meansassociated with said support structure means for establishing the secondcoordinate system including establishing a second plane of referencethat intersects the first plane of reference at a common point in bothsaid first and second planes of reference, adjustment means associatedwith said support structure means for establishing the direction inspace with respect to said first and second planes of reference, saiddirection in space passing through said common point, first and secondscale means including cooperating relatively movable members associatedwith the support structure means and with the movable means associatedtherewith for indicating respectively the angles theta and phi betweenthe first and second planes of reference, third and fourth scale meansincluding cooperating relatively movable members associated with thesupport structure means and with the adjustment means for indicatingrespectively the azimuth angle As and elevational angle Es of saiddirection in space with respect to said first plane of reference, andfifth and sixth scale means including cooperating relatively movablemembers associated with the movable means and with the adjustment meansfor indicating respectively the azimuth angle lambda a and the elevationangle lambda e of said direction in space with respect to said secondplane of reference, any two unknown variables of said six variablesbeing indicated by their respective scale means when the other fourscale means are indicating the other four variables.
 7. The meansdefined in claim 6 wherein said means for establishing the first planeof reference include a transparent member on which said third and fourthscale means are located.
 8. The means defined in claim 7 wherein saidtransparent member is shaped and positioned so that all points at whichsaid third and fourth scale means are located thereon are equidistantfrom said common point.
 9. The means defined in claim 6 wherein saidmeaNs for establishing said second plane of reference include a gimbalassembly on which said first, second, fifth and sixth scale means arelocated.
 10. Means for converting between a set of known and a set ofunknown coordinates, one set being the azimuth and elevation angles of adirection with respect to a first plane and the other set being theazimuth and elevation angles of the same direction with respect to asecond plane whose orientation is related to the orientation of thefirst plane by known angles established therebetween about two mutuallyperpendicular axes, said coordinate converting means including a gimbalassembly defining a center point therein through which saidperpendicular axes pass, said gimbal assembly including means tosimulate the aforesaid direction which passes through said center point,said gimbal assembly also including other means to simulate said secondplane, said other means being supported for movement about said centerpoint, scale means positioned to be intersected by said simulateddirection including a first set of scales, a portion of said first setof scales establishing the position of said first plane, said first setof scales being calibrated to indicate the azimuth and elevation anglesof said direction from said center point and relative to said firstplane, means associated with said gimbal assembly to establishpredetermined orientations of said second plane with respect to saidfirst plane, a second set of scales located on said gimbal assembly forindicating the angular relationships in azimuth and elevation angles ofsaid direction with respect to said second plane, said converting meansindicating the unknown set of coordinates when the known set ofcoordinates and the orientation of the second plane with respect to thefirst plane are established.
 11. The means defined in claim 10 whereinsaid means to establish predetermined orientations of said second planewith respect to said first plane include first and second gearassemblies, said first gear assembly being movable to angularly rotatesaid means to simulate said second plane about one of said mutuallyperpendicular axes and said second gear assembly being movable to rotatesaid means to simulate said second plane about the other of saidmutually perpendicular axes.
 12. The means defined in claim 10 whereinsaid first set of scales includes a scale for indicating the azimuthangle of said direction with respect to said first plane which scale isformed by a family of lines which are the lines of intersection betweensaid scale means and a family of coaxial planes whose common axis passesthrough said center point at right angles to said first plane.
 13. Themeans defined in claim 10 wherein said first set of scales includes ascale for indicating the elevation angle of said direction with respectto said first plane which scale is formed by a family of lines which arethe lines of intersection between said scale means and a family ofparallel planes including said first plane.
 14. The means defined inclaim 10 wherein said means for simulating the direction include apointer member pivotally connected to said gimbal assembly, said pointermember having means thereon engageable with said scale means to indicatethe set of coordinates of said direction in space relative to said firstplane, and wherein said gimbal assembly includes means thereon whichcooperate with said pointer member to indicate the set of coordinates ofsaid direction in space relative to said second plane.
 15. The meansdefined in claim 14 wherein said pointer member is counterbalanced.